Iran will top the agenda for U.S. Secretary of State Rex Tillerson as he heads to Europe next week for meetings with allies, a U.S. official said on January 19.

Tillerson's trip comes amid behind-the-scenes negotiations over the fate of the landmark agreement to curb Iran's nuclear program in exchange for easing crippling international sanctions targeting Tehran.

Earlier this month, U.S. President Donald Trump announced that he was prolonging U.S. sanctions imposed earlier against Iran. But Trump also said he wanted to work with European allies and Congress to fix what he called "disastrous flaws" in the 2015 Iran deal signed under his predecessor, Barack Obama.

Trump warned that Washington would withdraw from the deal if it is not strengthened within 120 days.

A State Department official, speaking on condition of anonymity, told reporters on January 19 that Iran would dominate Tillerson's meetings in Europe.

"As you know, we really emphasize close coordination with the British in particular and the French in our efforts to close the gaps in [the agreement] and in next steps on how we curtail Iranian malign influence in the region," the official told reporters. "So I think that'll be a very high priority in his conversations."

Russian Foreign Minister Sergei Lavrov, meanwhile, warned that the nuclear deal would collapse if the United States pulled out.

"This agreement cannot be implemented if one of the participants unilaterally steps out of it. It will fall apart, there will be no deal then," Lavrov told reporters at the United Nations in New York on January 19.

Tillerson will be visiting London, Paris, Warsaw, and Davos, Switzerland, during the trip.

The U.S. official said that while in Warsaw, Tillerson will be discussing the U.S. military presence in Poland, which has hosted U.S. and other allied troops following Russia's 2014 seizure of Ukraine's Crimean Peninsula and its backing of armed separatists in eastern Ukraine.